Prior techniques and arrangements for converting synchronous digital transmission signals to asynchronous digital signals are known. In recent digital transmission systems it has become important to smooth large gaps in a supplied data signal resulting from overhead bit removal and stuff bits. This is particularly important, for example, in converting a SONET STS-1 synchronous digital signal to a DS3 asynchronous digital signal. As is known, in the STS-1 signal format, so-called pointer adjustments are used to reconcile small phase and frequency differences between a clock signal derived from an incoming STS-1 signal and a local clock signal. These adjustments are made on a byte-wise basis and can be either positive or negative. During normal system operation, the pointer adjustments occur relatively infrequently. This causes a low frequency, relatively large peak-to-peak jitter component in the signal. When the system operation is degraded, pointer adjustments may occur more often. Thus, a wide range of pointer adjustment rates is possible. A so-called bit leaking technique in conjunction with a phase locked loop and a synchronizing elastic store has been proposed in an attempt at smoothing gaps in a data signal caused by the pointer adjustments in a SONET signal format. A bit leak is defined as one (1) bit of phase error being supplied to a phase locked loop. One of these techniques employs a bit-by-bit leaking adjustment so that a phase locked loop having a "wider" bandwidth may be employed in the desynchronizer. This bit-by-bit technique, however, does not adequately compensate for the full range of pointer adjustment rates which may occur. An attempt at compensating for the pointer adjustments employing an adaptive bit leaking arrangement has also been proposed. However, to the best of our knowledge the proposed adaptive bit leaking arrangements still cause excessive jitter to occur in the asynchronous digital signal, e.g., the DS3 signal, or just simply do not operate satisfactorily.